Ok i'm not an expert in remote starts but this is wut i think...

Answer this...does your cigarette lighter work when you use the remote start? No right because you need to turn the ignition to at the first click. Like the cigarette lighter, the radio turns on only when the ignition's at the first click. That's why you said your stereo turns on normally when you use the key. For your car, when you use the remote start, don't you have to put in the key like within 5 mins or else the engine shuts off?

If this really bothers you, you can bypass it but the cons to that is your radio is pretty much on 24/7. That means you can turn it on even when your engine's off and when you don't have the key in. This would be a problem only if your have an amp that's hooks up to the constant power of your radio.

Hope this explains your probs. Yea can't do much about it.